van Genuchten-Mualem Wetting Permeability
Calculate normalized van Genuchten-Mualem wetting relative permeability from effective wetting saturation and m, with fixed connectivity exponent one half.
Calculate normalized van Genuchten-Mualem wetting relative permeability from effective wetting saturation and m, with fixed connectivity exponent one half.
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Calculation context and source notes
Calculate normalized wetting-phase relative permeability using the van Genuchten-Mualem relation with pore-connectivity exponent one half. The nonlinear saturation term differs from a single Corey power and shares its shape parameter with the restricted capillary-pressure model.
Enter effective wetting saturation on the calibrated curve's normalization and m strictly between zero and one. Use the normalized output as a relative-permeability curve point, not as absolute permeability or phase mobility. The endpoint multiplier is fixed at unity in this evaluator.
Solves for
k_rw (fraction)
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Formula, variables, and sourceCheck the wetting endpoints and a curve point
At effective wetting saturation 0.5 and m = 0.5, S_e^(1/m) is 0.25. The bracket is 1 - sqrt(0.75), and multiplying its square by sqrt(0.5) gives 0.012691996. At zero effective wetting saturation the normalized permeability is zero; at full effective saturation it is one.
For m = 0.5, rationalizing the bracket gives S_e squared divided by [1 + sqrt(1 - S_e squared)]. This independent expression checks small-saturation values that would lose precision when subtracting two nearly equal numbers. The implementation uses stable logarithmic functions and handles the exact endpoints separately.
| Effective wetting saturation | Normalized k_rw, m = 0.5 |
|---|---|
| 0 | 0 |
| 0.5 | 0.012691996 |
| 1 | 1 |
Do not substitute a generic Corey power
Corey wetting relative permeability is a normalized saturation raised to a fitted power, possibly multiplied by an endpoint value. The van Genuchten-Mualem expression has an additional nested nonlinear bracket. Matching one point with a Corey power does not make the two models equivalent across the saturation interval.
Using the same m in capillary pressure and wetting relative permeability follows this restricted model, not a universal claim that one capillary fit predicts every rock's permeability curve. Preserve fluid system, rock condition, saturation normalization and measurement history when comparing with core data. A normalized endpoint of one may require separate calibration before a reservoir simulation uses the result.
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Worked explanations, controlled studies and printable exercises connected to this calculation.
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Formula, variables, and default calculation
Reproducible default result
With the default values shown below, the calculation returns k_rw = 0.012692 fraction. Defaults demonstrate the implementation; they are not recommended field values.
0.5
0.5
Input definitions
S_e
fractionEffective Wetting Saturation
m
dimensionlessShape Parameter (0 < m < 1; n = 1 / (1 - m))
Output definitions
k_rw
Normalized Wetting Relative Permeability
Engineering use, assumptions, and limits
Enter effective wetting saturation on the calibrated curve's normalization and m strictly between zero and one. Use the normalized output as a relative-permeability curve point, not as absolute permeability or phase mobility. The endpoint multiplier is fixed at unity in this evaluator.
Assumptions
- Effective wetting saturation is between zero and one and uses the endpoints of the selected curve.
- The pore-connectivity exponent is fixed at 1/2, the normalized wetting endpoint is one, and m = 1 - 1/n.
Limitations
- No endpoint scaling, fitted free-connectivity exponent, saturation hysteresis or three-phase extension is provided.
- Relative permeability alone does not give a phase rate; absolute permeability, viscosity, pressure drive and geometry remain necessary.
Common mistakes
- Interpreting the fraction output as permeability in mD or as mobility, which additionally divides by viscosity.
- Entering total water saturation or a Corey exponent in place of effective saturation or the van Genuchten m parameter.
Frequently asked questions
What inputs does the van Genuchten-Mualem Wetting Relative Permeability calculator need?
The calculation uses Effective Wetting Saturation (S_e), Shape Parameter (0 < m < 1; n = 1 / (1 - m)) (m). Enter values on the units shown beside each field.
What result does this calculator return?
The primary result is normalized wetting relative permeability in fraction. The formula section shows the declared relationship, variables, and a reproducible default calculation.
What should I check before using the result?
Confirm the unit basis, source applicability, and input quality. No endpoint scaling, fitted free-connectivity exponent, saturation hysteresis or three-phase extension is provided. Interpreting the fraction output as permeability in mD or as mobility, which additionally divides by viscosity.
Source and record status
Source metadata identifies the relationship implemented by the calculator. Check the cited edition, unit basis, and scope against the engineering case before operational use.
PorousFlowVanGenuchten.h: relativePermeability, Idaho National Laboratory MOOSE contributors
Idaho National Laboratory MOOSE PorousFlowVanGenuchten::relativePermeability implementation, pinned revision c2fbc1e15048f5b43a5b80018f6ca63723757e62: sqrt(seff) times [1-(1-seff^(1/m))^m]^2.
Open source reference